Particle-Gas Dynamics with Athena: Method and Convergence

TL;DR

This paper presents a new hybrid particle-gas simulation scheme in Athena, demonstrating its stability, convergence, and application to studying streaming instability in protoplanetary disks, with insights into particle clumping and transport.

Contribution

It introduces a second order predictor-corrector hybrid scheme with semi-implicit and fully-implicit integrators for particle-gas dynamics in Athena, ensuring conservation and stability across regimes.

Findings

Gas flow properties converge at modest resolution.

Particle clumping requires higher resolution to converge.

Particle transport measurements may have ~20% error.

Abstract

The Athena MHD code has been extended to integrates the motion of particles coupled with the gas via aerodynamic drag, in order to study the dynamics of gas and solids in protoplanetary disks and the formation of planetesimals. Our particle-gas hybrid scheme is based on a second order predictor-corrector method. Careful treatment of the momentum feedback on the gas guarantees exact conservation. The hybrid scheme is stable and convergent in most regimes relevant to protoplanetary disks. We describe a semi-implicit integrator generalized from the leap-frog approach. In the absence of drag force, it preserves the geometric properties of a particle orbit. We also present a fully-implicit integrator that is unconditionally stable for all regimes of particle-gas coupling. Using our hybrid code, we study the numerical convergence of the non-linear saturated state of the streaming instability. We find that gas flow properties are well converged with modest grid resolution (128 cells per pressure length \eta r for dimensionless stopping time tau_s=0.1), and equal number of particles and grid cells. On the other hand, particle clumping properties converge only at higher resolutions, and finer resolution leads to stronger clumping before convergence is reached. Finally, we find that measurement of particle transport properties resulted from the streaming instability may be subject to error of about 20%.